Still without salary-cap space to attract major free agents and with a roster that will undergo more changes before training camp, the Celtics made two more additions Monday, officially signing Brazilian big man Vitor Faverani and guard Phil Pressey to guaranteed contracts.

Neither player appeared in Boston’s plans a month ago, but with the rebuild underway and the club looking to attract cheaper, younger talent, they could play pivotal roles.

Faverani is a 6-foot-11-inch center who played last year for Valencia Basket Club of the Spanish ACB League, averaging 9.3 points and 4.6 rebounds in 17 minutes in 23 games. He was eligible for the 2009 draft but was not selected. He has been on the Celtics’ radar for years and the deal is believed to be three years at $6 million.

Pressey is a 5-11 guard from Missouri with local ties, having played at Waltham High and for an AAU team in Boston while his father, former NBA player Paul Pressey, was a Celtics assistant under Doc Rivers.

Pressey went undrafted
last month but made such a positive impression during summer league that the club began negotiating a deal earlier this month. The sides agreed to what is believed to be a multiyear contract with guaranteed money.

Pressey could be the team’s long-desired backup point guard to Rajon Rondo and could have a major role early in the season as Rondo recovers from a torn right anterior cruciate ligament. The Celtics have lacked a dependable reserve point guard for years, leaning on Avery Bradley, Jason Terry, and others to spell Rondo.

Pressey is a legitimate point guard with the ability to score. He was a favorite of new Celtics coach Brad Stevens during summer league. On more than one occasion Stevens spoke of Pressey when mentioning the team’s other rookies — Kelly Olynyk and Colton Iverson.

The Celtics’ roster now stands at 17, meaning they will need to remove three players before opening night. They will have until Aug. 1 to make a decision on the contract of center Shavlik Randolph, who played well in limited action last season.

Depending on how he fares in camp, Faverani could be the starting center. By trading Kevin Garnett to the Nets, the Celtics lack a proven center. The future of Fab Melo, who is still considered a long-term project by the organization, is in question.

The Celtics could go small with Olynyk at center on occasion with Jared Sullinger and Brandon Bass at power forward along with Kris Humphries, but president of basketball operations Danny Ainge promised more changes to reduce the salary cap and avoid being a luxury tax repeater.

By adding the salaries of Humphries, Gerald Wallace, and Keith Bogans, the Celtics remain slightly over the cap and will have to find creative ways to get under by moving players for draft picks.